﻿ The graph of y = p(x) are given in the figure below, for some polynomials p(x). Find the number of zeroes of p(x), in each case. from Mathematics Polynomials Class 10 Uttarakhand Board Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. We have,
4u2 + 8u = 4u (u + 2)
So, the value of 4u2 + 8u is zero when 4u = 0 or u + 2 = 0
i.e., when u = 0 or u = –2
Therefore, the zeroes of 4u2 + 8u are 0 and - 2
Now,
Sum of zeroes = 0 + (-2) =  Product of zeroes = 0(-2) = = 870 Views

# The graph of y = p(x) are given in the figure below, for some polynomials p(x). Find the number of zeroes of p(x), in each case. (i) Graph y = p(x) does not cut the x-axis at any point, so the given polynomial has no zero. (ii) Graph y = p(x) cuts the x-axis at one point, so the given polynomial has one zero. (iii) Graph y = p(x) cuts the x-axis at three points, so the given polynomial has three zeroes. (iv) Graph y = p(x) cuts the x-axis at two points, so the given polynomial has two zeroes. (v) Graph y = p(x) cuts the x-axis at four points, so the given polynomial has four zeroes. (vi) Graph y = p(x) cuts the x-axis at three points, so the given polynomial has three zeroes.
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Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. We have,6x2–7x–3 = 6x2– 9x + 2x – 3
= 3x(2x – 3) + 1(2x – 3)
= (3x + 1) (2x – 3)
So, the value of 6x2 – 7 – 3 is zero when (3a + 1) = 0 or (2x – 3) = 0
i.e. Now,
Sum of zeroes  =  Product of zeroes = = 862 Views

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. We have,
4s2 – 4s + 1 = 4s2 – 2s –2s + 1 = (2s–1)(2s– 1)
So, the value of 4s2 – 4s + 1 is zero, when 2s – 1 = 0 or 2s – 1 = 0
i.e.  when Therefore, the zeroes of 4s2 – 4s + 1 are Now,
Sum of zeroes =  Product of zeroes  =  791 Views

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. We have,  So, the value of x2 – 2x - 8 is zero when x - 4 = 0 or x + 2 = 0.
i.e., when x = 4 or x = –2.
Therefore, the zeroes of x2 – 2x – 8 are 4 and - 2. Now,
Sum of zeroes = (4) + (-2) Product of zeroes = (4) (-2) 931 Views